A selected matching and an ansatz-feasibility problem

The auxiliary inner product is a mathematical comparison device, not an extracted physical metric.

The theorem is useful only after $X,L,s$ have been fixed. Theorem thm:surjective shows why allowing every independent point jet makes the pointwise feasibility question automatic. Operationally derived restrictions or field compatibility conditions must carry the substantive content.

A witness for a fixed ansatz is not a no-go theorem for every possible carrier extension, source interpretation, or geometric rule.